Theorem cmetmeti

Description: A complete metric space is a metric space. (Contributed by NM, 26-Oct-2007)

	Ref	Expression
Hypothesis	cmetmeti.1	⊢ 𝐷 ∈ ( CMet ‘ 𝑋 )
Assertion	cmetmeti	⊢ 𝐷 ∈ ( Met ‘ 𝑋 )

Proof

Step	Hyp	Ref	Expression
1		cmetmeti.1	⊢ 𝐷 ∈ ( CMet ‘ 𝑋 )
2		cmetmet	⊢ ( 𝐷 ∈ ( CMet ‘ 𝑋 ) → 𝐷 ∈ ( Met ‘ 𝑋 ) )
3	1 2	ax-mp	⊢ 𝐷 ∈ ( Met ‘ 𝑋 )